Compare the obtained computational results with infinite

Question

Project 1

Complete parts 1A, 1B, and 1C

Prepare a report describing your steps and results

Send by email a zip or rar file that contains the report and all MATLAB files you have used.

Project 1A:

In this project, we consider a circular disk of radius a, which is uniformly charged with ρ_s C/m². The disk lies on the z=0 plane with its axis along the z-axis.

The provided MATLAB program calculates the electric fieldE at point A(0,0,h). The computation depends on discretizing the disk into small squares with side lengthd.

Project steps:

1. Use the program to obtain E at point A. Consider a disk of radius a = 1m and the discretization size d = 0.1. Consider two different values of h: 1 cm, and 1 m.

2. Choose the value of ρs to be 63μC/m².

3. Compare the obtained computational results with infinite surface charge approximation.

4. Derive an analytical expression of flux density E at point A. Show that:

E= ρ_s/(2ε₀ ) {1-h/√(h² + a² )} a_z

5. Compare the computational results with the analytical solution. (Calculate the percentage error for each value of h).

6. Repeat part 5, using d =1 mm. Compare the computation time of part 5 and part 6.

Project 1B:

This project considers applying the boundary conditions on the boundary between two different media. Considering ε_r1=2 and ε_r2=3, use the given MATLAB program of Project1B to calculate the following fields:

E₂ given that E₁ = 3a_x + 4a_y + 5a_z.
E₁ given that E₂ = 3a_x + 4a_y + 5a_z.

Project 1C:

Consider a uniform line charge of ρ_L= XXμC/m is located on the z-axis in the region -1

Attachment:- Assignment.rar